DEAN, David S.; GUÉRIN, Thomas

doi:10.1103/PhysRevE.90.062114

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DEAN, David S.
Laboratoire Ondes et Matière d'Aquitaine [LOMA]

GUÉRIN, Thomas
Laboratoire Ondes et Matière d'Aquitaine [LOMA]

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Physical Review E : Statistical, Nonlinear, and Soft Matter Physics. 2014-12-08, vol. 90, n° 6, p. 062114 (1-6)

American Physical Society

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We analyze the mean squared displacement of a Brownian particle in a medium with a spatially varying local diffusivity which is assumed to be periodic. When the system is asymptotically diffusive the mean squared displacement, characterizing the dispersion in the system, is, at late times, a linear function of time. A Kubo type formula is given for the mean squared displacement which allows the recovery of some known results for the effective diffusion constant $D_e$ in a direct way, but also allows an understanding of the asymptotic approach to the diffusive limit. In particular, as well as as computing the slope of a linear fit to the late time mean squared displacement, we find a formula for the constant where the fit intersects the y axis.< Réduire

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Stochastic analysis methods

Stochastic processes

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Approach to asymptotically diffusive behavior for Brownian particles in media with periodic diffusivities

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